Properties

Label 368.2.i.b.91.6
Level 368368
Weight 22
Character 368.91
Analytic conductor 2.9382.938
Analytic rank 00
Dimension 8080
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [368,2,Mod(91,368)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(368, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("368.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 368=2423 368 = 2^{4} \cdot 23
Weight: k k == 2 2
Character orbit: [χ][\chi] == 368.i (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.938494794382.93849479438
Analytic rank: 00
Dimension: 8080
Relative dimension: 4040 over Q(i)\Q(i)
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 91.6
Character χ\chi == 368.91
Dual form 368.2.i.b.275.6

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.338670.456028i)q2+(0.860099+0.860099i)q3+(1.58408+1.22094i)q4+(0.05926280.0592628i)q5+(0.7591601.54362i)q6+2.65917iq7+(1.563772.35682i)q81.52046iq9+(0.106359+0.0523078i)q10+(3.23118+3.23118i)q11+(0.312330+2.41260i)q12+(1.324951.32495i)q13+(1.212663.55975i)q14+0.101944q15+(1.01859+3.86813i)q16+1.27002iq17+(0.693372+2.03539i)q18+(4.69664+4.69664i)q19+(0.1662330.0215203i)q20+(2.28715+2.28715i)q21+(2.851975.79899i)q22+(2.501754.09161i)q23+(0.6821053.37210i)q24+4.99298iq25+(2.37788+1.16946i)q26+(3.888043.88804i)q27+(3.24670+4.21233i)q28+(1.21823+1.21823i)q29+(0.1364690.0464892i)q30+2.31556iq31+(0.4004175.64266i)q32+5.55826iq33+(0.5791651.70014i)q34+(0.157590+0.157590i)q35+(1.856392.40852i)q36+(1.54778+1.54778i)q37+(8.429054.14545i)q38+2.27918q39+(0.2323450.0469985i)q40+2.46013iq41+(4.104742.01873i)q42+(8.21821+8.21821i)q43+(1.17335+9.06351i)q44+(0.09010660.0901066i)q45+(5.21491+4.33645i)q461.72980iq47+(2.45089+4.20307i)q480.0711808q49+(2.276946.68395i)q50+(1.09234+1.09234i)q51+(3.716510.481132i)q52+(5.850765.85076i)q53+(6.97787+3.43175i)q54+0.382977q55+(6.267194.15833i)q568.07915q57+(2.186351.07526i)q58+(10.222610.2226i)q59+(0.161487+0.124468i)q60+(9.184239.18423i)q61+(1.055963.09978i)q62+4.04316q63+(3.10924+7.37107i)q640.157040iq65+(2.534737.44068i)q66+(0.2410490.241049i)q67+(1.55062+2.01181i)q68+(5.670941.36744i)q69+(0.1390950.282826i)q7015.0134q71+(3.58345+2.37765i)q722.20672iq73+(2.777811.36614i)q74+(4.29446+4.29446i)q75+(13.1742+1.70550i)q76+(8.59224+8.59224i)q77+(3.051071.03937i)q786.90459q79+(0.289601+0.168872i)q80+2.12683q81+(1.121893.29330i)q82+(6.962626.96262i)q83+(6.41550+0.830539i)q84+(0.0752648+0.0752648i)q85+(7.2537314.7492i)q862.09559q87+(2.5625012.6681i)q8814.2609q89+(0.0795318+0.161714i)q90+(3.52326+3.52326i)q91+(8.958583.42693i)q92+(1.99162+1.99162i)q93+(0.788838+2.31563i)q94+0.556672iq95+(5.197654.50885i)q967.99512iq97+(0.0952876+0.0324605i)q98+(4.912874.91287i)q99+O(q100)q+(-1.33867 - 0.456028i) q^{2} +(0.860099 + 0.860099i) q^{3} +(1.58408 + 1.22094i) q^{4} +(0.0592628 - 0.0592628i) q^{5} +(-0.759160 - 1.54362i) q^{6} +2.65917i q^{7} +(-1.56377 - 2.35682i) q^{8} -1.52046i q^{9} +(-0.106359 + 0.0523078i) q^{10} +(3.23118 + 3.23118i) q^{11} +(0.312330 + 2.41260i) q^{12} +(1.32495 - 1.32495i) q^{13} +(1.21266 - 3.55975i) q^{14} +0.101944 q^{15} +(1.01859 + 3.86813i) q^{16} +1.27002i q^{17} +(-0.693372 + 2.03539i) q^{18} +(-4.69664 + 4.69664i) q^{19} +(0.166233 - 0.0215203i) q^{20} +(-2.28715 + 2.28715i) q^{21} +(-2.85197 - 5.79899i) q^{22} +(2.50175 - 4.09161i) q^{23} +(0.682105 - 3.37210i) q^{24} +4.99298i q^{25} +(-2.37788 + 1.16946i) q^{26} +(3.88804 - 3.88804i) q^{27} +(-3.24670 + 4.21233i) q^{28} +(-1.21823 + 1.21823i) q^{29} +(-0.136469 - 0.0464892i) q^{30} +2.31556i q^{31} +(0.400417 - 5.64266i) q^{32} +5.55826i q^{33} +(0.579165 - 1.70014i) q^{34} +(0.157590 + 0.157590i) q^{35} +(1.85639 - 2.40852i) q^{36} +(-1.54778 + 1.54778i) q^{37} +(8.42905 - 4.14545i) q^{38} +2.27918 q^{39} +(-0.232345 - 0.0469985i) q^{40} +2.46013i q^{41} +(4.10474 - 2.01873i) q^{42} +(8.21821 + 8.21821i) q^{43} +(1.17335 + 9.06351i) q^{44} +(-0.0901066 - 0.0901066i) q^{45} +(-5.21491 + 4.33645i) q^{46} -1.72980i q^{47} +(-2.45089 + 4.20307i) q^{48} -0.0711808 q^{49} +(2.27694 - 6.68395i) q^{50} +(-1.09234 + 1.09234i) q^{51} +(3.71651 - 0.481132i) q^{52} +(5.85076 - 5.85076i) q^{53} +(-6.97787 + 3.43175i) q^{54} +0.382977 q^{55} +(6.26719 - 4.15833i) q^{56} -8.07915 q^{57} +(2.18635 - 1.07526i) q^{58} +(10.2226 - 10.2226i) q^{59} +(0.161487 + 0.124468i) q^{60} +(-9.18423 - 9.18423i) q^{61} +(1.05596 - 3.09978i) q^{62} +4.04316 q^{63} +(-3.10924 + 7.37107i) q^{64} -0.157040i q^{65} +(2.53473 - 7.44068i) q^{66} +(0.241049 - 0.241049i) q^{67} +(-1.55062 + 2.01181i) q^{68} +(5.67094 - 1.36744i) q^{69} +(-0.139095 - 0.282826i) q^{70} -15.0134 q^{71} +(-3.58345 + 2.37765i) q^{72} -2.20672i q^{73} +(2.77781 - 1.36614i) q^{74} +(-4.29446 + 4.29446i) q^{75} +(-13.1742 + 1.70550i) q^{76} +(-8.59224 + 8.59224i) q^{77} +(-3.05107 - 1.03937i) q^{78} -6.90459 q^{79} +(0.289601 + 0.168872i) q^{80} +2.12683 q^{81} +(1.12189 - 3.29330i) q^{82} +(6.96262 - 6.96262i) q^{83} +(-6.41550 + 0.830539i) q^{84} +(0.0752648 + 0.0752648i) q^{85} +(-7.25373 - 14.7492i) q^{86} -2.09559 q^{87} +(2.56250 - 12.6681i) q^{88} -14.2609 q^{89} +(0.0795318 + 0.161714i) q^{90} +(3.52326 + 3.52326i) q^{91} +(8.95858 - 3.42693i) q^{92} +(-1.99162 + 1.99162i) q^{93} +(-0.788838 + 2.31563i) q^{94} +0.556672i q^{95} +(5.19765 - 4.50885i) q^{96} -7.99512i q^{97} +(0.0952876 + 0.0324605i) q^{98} +(4.91287 - 4.91287i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 80q4q24q316q64q8+20q124q1316q16+24q18+4q23+4q2424q26+44q2720q2924q32+16q35+104q36128q3916q46+88q98+O(q100) 80 q - 4 q^{2} - 4 q^{3} - 16 q^{6} - 4 q^{8} + 20 q^{12} - 4 q^{13} - 16 q^{16} + 24 q^{18} + 4 q^{23} + 4 q^{24} - 24 q^{26} + 44 q^{27} - 20 q^{29} - 24 q^{32} + 16 q^{35} + 104 q^{36} - 128 q^{39} - 16 q^{46}+ \cdots - 88 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/368Z)×\left(\mathbb{Z}/368\mathbb{Z}\right)^\times.

nn 4747 9797 277277
χ(n)\chi(n) 1-1 1-1 e(14)e\left(\frac{1}{4}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.33867 0.456028i −0.946583 0.322461i
33 0.860099 + 0.860099i 0.496579 + 0.496579i 0.910371 0.413793i 0.135796π-0.135796\pi
−0.413793 + 0.910371i 0.635796π0.635796\pi
44 1.58408 + 1.22094i 0.792038 + 0.610472i
55 0.0592628 0.0592628i 0.0265031 0.0265031i −0.693731 0.720234i 0.744034π-0.744034\pi
0.720234 + 0.693731i 0.244034π0.244034\pi
66 −0.759160 1.54362i −0.309926 0.630180i
77 2.65917i 1.00507i 0.864556 + 0.502536i 0.167599π0.167599\pi
−0.864556 + 0.502536i 0.832401π0.832401\pi
88 −1.56377 2.35682i −0.552876 0.833263i
99 1.52046i 0.506819i
1010 −0.106359 + 0.0523078i −0.0336336 + 0.0165412i
1111 3.23118 + 3.23118i 0.974236 + 0.974236i 0.999676 0.0254403i 0.00809877π-0.00809877\pi
−0.0254403 + 0.999676i 0.508099π0.508099\pi
1212 0.312330 + 2.41260i 0.0901620 + 0.696456i
1313 1.32495 1.32495i 0.367475 0.367475i −0.499081 0.866555i 0.666329π-0.666329\pi
0.866555 + 0.499081i 0.166329π0.166329\pi
1414 1.21266 3.55975i 0.324096 0.951383i
1515 0.101944 0.0263218
1616 1.01859 + 3.86813i 0.254649 + 0.967034i
1717 1.27002i 0.308025i 0.988069 + 0.154012i 0.0492196π0.0492196\pi
−0.988069 + 0.154012i 0.950780π0.950780\pi
1818 −0.693372 + 2.03539i −0.163429 + 0.479747i
1919 −4.69664 + 4.69664i −1.07748 + 1.07748i −0.0807484 + 0.996735i 0.525731π0.525731\pi
−0.996735 + 0.0807484i 0.974269π0.974269\pi
2020 0.166233 0.0215203i 0.0371709 0.00481208i
2121 −2.28715 + 2.28715i −0.499097 + 0.499097i
2222 −2.85197 5.79899i −0.608042 1.23635i
2323 2.50175 4.09161i 0.521651 0.853159i
2424 0.682105 3.37210i 0.139234 0.688327i
2525 4.99298i 0.998595i
2626 −2.37788 + 1.16946i −0.466342 + 0.229349i
2727 3.88804 3.88804i 0.748254 0.748254i
2828 −3.24670 + 4.21233i −0.613568 + 0.796055i
2929 −1.21823 + 1.21823i −0.226219 + 0.226219i −0.811111 0.584892i 0.801137π-0.801137\pi
0.584892 + 0.811111i 0.301137π0.301137\pi
3030 −0.136469 0.0464892i −0.0249157 0.00848774i
3131 2.31556i 0.415888i 0.978141 + 0.207944i 0.0666771π0.0666771\pi
−0.978141 + 0.207944i 0.933323π0.933323\pi
3232 0.400417 5.64266i 0.0707844 0.997492i
3333 5.55826i 0.967570i
3434 0.579165 1.70014i 0.0993259 0.291571i
3535 0.157590 + 0.157590i 0.0266375 + 0.0266375i
3636 1.85639 2.40852i 0.309399 0.401420i
3737 −1.54778 + 1.54778i −0.254454 + 0.254454i −0.822794 0.568340i 0.807586π-0.807586\pi
0.568340 + 0.822794i 0.307586π0.307586\pi
3838 8.42905 4.14545i 1.36737 0.672481i
3939 2.27918 0.364960
4040 −0.232345 0.0469985i −0.0367370 0.00743112i
4141 2.46013i 0.384208i 0.981375 + 0.192104i 0.0615310π0.0615310\pi
−0.981375 + 0.192104i 0.938469π0.938469\pi
4242 4.10474 2.01873i 0.633376 0.311497i
4343 8.21821 + 8.21821i 1.25326 + 1.25326i 0.954248 + 0.299017i 0.0966588π0.0966588\pi
0.299017 + 0.954248i 0.403341π0.403341\pi
4444 1.17335 + 9.06351i 0.176889 + 1.36638i
4545 −0.0901066 0.0901066i −0.0134323 0.0134323i
4646 −5.21491 + 4.33645i −0.768896 + 0.639374i
4747 1.72980i 0.252317i −0.992010 0.126159i 0.959735π-0.959735\pi
0.992010 0.126159i 0.0402648π-0.0402648\pi
4848 −2.45089 + 4.20307i −0.353755 + 0.606661i
4949 −0.0711808 −0.0101687
5050 2.27694 6.68395i 0.322008 0.945253i
5151 −1.09234 + 1.09234i −0.152959 + 0.152959i
5252 3.71651 0.481132i 0.515387 0.0667211i
5353 5.85076 5.85076i 0.803663 0.803663i −0.180003 0.983666i 0.557611π-0.557611\pi
0.983666 + 0.180003i 0.0576106π0.0576106\pi
5454 −6.97787 + 3.43175i −0.949567 + 0.467002i
5555 0.382977 0.0516406
5656 6.26719 4.15833i 0.837489 0.555680i
5757 −8.07915 −1.07011
5858 2.18635 1.07526i 0.287082 0.141188i
5959 10.2226 10.2226i 1.33088 1.33088i 0.426287 0.904588i 0.359821π-0.359821\pi
0.904588 0.426287i 0.140179π-0.140179\pi
6060 0.161487 + 0.124468i 0.0208478 + 0.0160687i
6161 −9.18423 9.18423i −1.17592 1.17592i −0.980774 0.195146i 0.937482π-0.937482\pi
−0.195146 0.980774i 0.562518π-0.562518\pi
6262 1.05596 3.09978i 0.134107 0.393672i
6363 4.04316 0.509390
6464 −3.10924 + 7.37107i −0.388655 + 0.921383i
6565 0.157040i 0.0194785i
6666 2.53473 7.44068i 0.312003 0.915885i
6767 0.241049 0.241049i 0.0294489 0.0294489i −0.692229 0.721678i 0.743371π-0.743371\pi
0.721678 + 0.692229i 0.243371π0.243371\pi
6868 −1.55062 + 2.01181i −0.188040 + 0.243967i
6969 5.67094 1.36744i 0.682701 0.164620i
7070 −0.139095 0.282826i −0.0166251 0.0338042i
7171 −15.0134 −1.78176 −0.890879 0.454241i 0.849911π-0.849911\pi
−0.890879 + 0.454241i 0.849911π0.849911\pi
7272 −3.58345 + 2.37765i −0.422314 + 0.280208i
7373 2.20672i 0.258277i −0.991627 0.129139i 0.958779π-0.958779\pi
0.991627 0.129139i 0.0412212π-0.0412212\pi
7474 2.77781 1.36614i 0.322913 0.158810i
7575 −4.29446 + 4.29446i −0.495881 + 0.495881i
7676 −13.1742 + 1.70550i −1.51118 + 0.195635i
7777 −8.59224 + 8.59224i −0.979177 + 0.979177i
7878 −3.05107 1.03937i −0.345465 0.117685i
7979 −6.90459 −0.776827 −0.388414 0.921485i 0.626977π-0.626977\pi
−0.388414 + 0.921485i 0.626977π0.626977\pi
8080 0.289601 + 0.168872i 0.0323784 + 0.0188804i
8181 2.12683 0.236315
8282 1.12189 3.29330i 0.123892 0.363684i
8383 6.96262 6.96262i 0.764247 0.764247i −0.212840 0.977087i 0.568271π-0.568271\pi
0.977087 + 0.212840i 0.0682714π0.0682714\pi
8484 −6.41550 + 0.830539i −0.699988 + 0.0906192i
8585 0.0752648 + 0.0752648i 0.00816362 + 0.00816362i
8686 −7.25373 14.7492i −0.782190 1.59045i
8787 −2.09559 −0.224671
8888 2.56250 12.6681i 0.273163 1.35043i
8989 −14.2609 −1.51166 −0.755828 0.654771i 0.772765π-0.772765\pi
−0.755828 + 0.654771i 0.772765π0.772765\pi
9090 0.0795318 + 0.161714i 0.00838339 + 0.0170462i
9191 3.52326 + 3.52326i 0.369338 + 0.369338i
9292 8.95858 3.42693i 0.933997 0.357282i
9393 −1.99162 + 1.99162i −0.206521 + 0.206521i
9494 −0.788838 + 2.31563i −0.0813625 + 0.238839i
9595 0.556672i 0.0571133i
9696 5.19765 4.50885i 0.530483 0.460183i
9797 7.99512i 0.811781i −0.913922 0.405891i 0.866961π-0.866961\pi
0.913922 0.405891i 0.133039π-0.133039\pi
9898 0.0952876 + 0.0324605i 0.00962550 + 0.00327900i
9999 4.91287 4.91287i 0.493762 0.493762i
100100 −6.09614 + 7.90925i −0.609614 + 0.790925i
101101 −3.64570 3.64570i −0.362760 0.362760i 0.502068 0.864828i 0.332573π-0.332573\pi
−0.864828 + 0.502068i 0.832573π0.832573\pi
102102 1.96043 0.964147i 0.194111 0.0954648i
103103 13.3253i 1.31298i −0.754333 0.656492i 0.772039π-0.772039\pi
0.754333 0.656492i 0.227961π-0.227961\pi
104104 −5.19459 1.05076i −0.509371 0.103035i
105105 0.271086i 0.0264553i
106106 −10.5003 + 5.16412i −1.01988 + 0.501584i
107107 7.02903 + 7.02903i 0.679522 + 0.679522i 0.959892 0.280370i 0.0904570π-0.0904570\pi
−0.280370 + 0.959892i 0.590457π0.590457\pi
108108 10.9060 1.41188i 1.04943 0.135858i
109109 −3.12657 3.12657i −0.299471 0.299471i 0.541335 0.840807i 0.317919π-0.317919\pi
−0.840807 + 0.541335i 0.817919π0.817919\pi
110110 −0.512680 0.174648i −0.0488821 0.0166521i
111111 −2.66250 −0.252713
112112 −10.2860 + 2.70862i −0.971938 + 0.255940i
113113 8.66950i 0.815558i −0.913081 0.407779i 0.866303π-0.866303\pi
0.913081 0.407779i 0.133697π-0.133697\pi
114114 10.8153 + 3.68432i 1.01295 + 0.345069i
115115 −0.0942195 0.390741i −0.00878601 0.0364367i
116116 −3.41715 + 0.442378i −0.317274 + 0.0410738i
117117 −2.01453 2.01453i −0.186243 0.186243i
118118 −18.3466 + 9.02293i −1.68894 + 0.830628i
119119 −3.37719 −0.309587
120120 −0.159417 0.240263i −0.0145527 0.0219330i
121121 9.88099i 0.898272i
122122 8.10638 + 16.4829i 0.733918 + 1.49229i
123123 −2.11596 + 2.11596i −0.190789 + 0.190789i
124124 −2.82717 + 3.66803i −0.253888 + 0.329399i
125125 0.592211 + 0.592211i 0.0529690 + 0.0529690i
126126 −5.41245 1.84379i −0.482180 0.164258i
127127 5.22135i 0.463320i −0.972797 0.231660i 0.925584π-0.925584\pi
0.972797 0.231660i 0.0744157π-0.0744157\pi
128128 7.52367 8.44952i 0.665004 0.746839i
129129 14.1370i 1.24469i
130130 −0.0716148 + 0.210225i −0.00628104 + 0.0184380i
131131 3.33453 + 3.33453i 0.291339 + 0.291339i 0.837609 0.546270i 0.183953π-0.183953\pi
−0.546270 + 0.837609i 0.683953π0.683953\pi
132132 −6.78633 + 8.80471i −0.590674 + 0.766352i
133133 −12.4892 12.4892i −1.08295 1.08295i
134134 −0.432611 + 0.212760i −0.0373719 + 0.0183797i
135135 0.460832i 0.0396621i
136136 2.99321 1.98602i 0.256666 0.170300i
137137 −7.42500 −0.634361 −0.317180 0.948365i 0.602736π-0.602736\pi
−0.317180 + 0.948365i 0.602736π0.602736\pi
138138 −8.21511 0.755563i −0.699317 0.0643178i
139139 6.66197 6.66197i 0.565061 0.565061i −0.365680 0.930741i 0.619164π-0.619164\pi
0.930741 + 0.365680i 0.119164π0.119164\pi
140140 0.0572260 + 0.442042i 0.00483648 + 0.0373594i
141141 1.48780 1.48780i 0.125295 0.125295i
142142 20.0979 + 6.84652i 1.68658 + 0.574547i
143143 8.56229 0.716014
144144 5.88134 1.54873i 0.490111 0.129061i
145145 0.144391i 0.0119910i
146146 −1.00633 + 2.95407i −0.0832843 + 0.244481i
147147 −0.0612226 0.0612226i −0.00504955 0.00504955i
148148 −4.34156 + 0.562051i −0.356874 + 0.0462003i
149149 6.57835 6.57835i 0.538920 0.538920i −0.384292 0.923212i 0.625554π-0.625554\pi
0.923212 + 0.384292i 0.125554π0.125554\pi
150150 7.70725 3.79047i 0.629295 0.309490i
151151 15.6057 1.26997 0.634986 0.772524i 0.281006π-0.281006\pi
0.634986 + 0.772524i 0.281006π0.281006\pi
152152 18.4136 + 3.72469i 1.49354 + 0.302112i
153153 1.93101 0.156113
154154 15.4205 7.58387i 1.24262 0.611126i
155155 0.137227 + 0.137227i 0.0110223 + 0.0110223i
156156 3.61039 + 2.78274i 0.289062 + 0.222798i
157157 6.05567 + 6.05567i 0.483295 + 0.483295i 0.906182 0.422887i 0.138983π-0.138983\pi
−0.422887 + 0.906182i 0.638983π0.638983\pi
158158 9.24297 + 3.14869i 0.735331 + 0.250496i
159159 10.0645 0.798164
160160 −0.310670 0.358130i −0.0245606 0.0283126i
161161 10.8803 + 6.65257i 0.857486 + 0.524296i
162162 −2.84713 0.969896i −0.223692 0.0762022i
163163 −10.7888 10.7888i −0.845040 0.845040i 0.144469 0.989509i 0.453853π-0.453853\pi
−0.989509 + 0.144469i 0.953853π0.953853\pi
164164 −3.00368 + 3.89703i −0.234548 + 0.304307i
165165 0.329398 + 0.329398i 0.0256436 + 0.0256436i
166166 −12.4958 + 6.14550i −0.969862 + 0.476983i
167167 −6.67959 −0.516882 −0.258441 0.966027i 0.583209π-0.583209\pi
−0.258441 + 0.966027i 0.583209π0.583209\pi
168168 8.96699 + 1.81383i 0.691818 + 0.139940i
169169 9.48902i 0.729925i
170170 −0.0664319 0.135078i −0.00509509 0.0103600i
171171 7.14104 + 7.14104i 0.546089 + 0.546089i
172172 2.98430 + 23.0522i 0.227551 + 1.75772i
173173 9.10911 9.10911i 0.692553 0.692553i −0.270240 0.962793i 0.587103π-0.587103\pi
0.962793 + 0.270240i 0.0871030π0.0871030\pi
174174 2.80531 + 0.955650i 0.212670 + 0.0724476i
175175 −13.2772 −1.00366
176176 −9.20736 + 15.7899i −0.694031 + 1.19021i
177177 17.5850 1.32177
178178 19.0907 + 6.50339i 1.43091 + 0.487449i
179179 0.0909711 + 0.0909711i 0.00679950 + 0.00679950i 0.710498 0.703699i 0.248470π-0.248470\pi
−0.703699 + 0.710498i 0.748470π0.748470\pi
180180 −0.0327206 0.252751i −0.00243885 0.0188389i
181181 11.3170 11.3170i 0.841187 0.841187i −0.147826 0.989013i 0.547228π-0.547228\pi
0.989013 + 0.147826i 0.0472276π0.0472276\pi
182182 −3.10978 6.32320i −0.230512 0.468707i
183183 15.7987i 1.16787i
184184 −13.5554 + 0.502156i −0.999315 + 0.0370194i
185185 0.183452i 0.0134877i
186186 3.57435 1.75788i 0.262084 0.128894i
187187 −4.10365 + 4.10365i −0.300089 + 0.300089i
188188 2.11199 2.74014i 0.154033 0.199845i
189189 10.3390 + 10.3390i 0.752049 + 0.752049i
190190 0.253858 0.745200i 0.0184168 0.0540625i
191191 −15.7543 −1.13994 −0.569972 0.821664i 0.693046π-0.693046\pi
−0.569972 + 0.821664i 0.693046π0.693046\pi
192192 −9.01411 + 3.66559i −0.650537 + 0.264541i
193193 −9.94979 −0.716202 −0.358101 0.933683i 0.616576π-0.616576\pi
−0.358101 + 0.933683i 0.616576π0.616576\pi
194194 −3.64600 + 10.7028i −0.261768 + 0.768418i
195195 0.135070 0.135070i 0.00967258 0.00967258i
196196 −0.112756 0.0869077i −0.00805399 0.00620770i
197197 12.0238 + 12.0238i 0.856661 + 0.856661i 0.990943 0.134282i 0.0428729π-0.0428729\pi
−0.134282 + 0.990943i 0.542873π0.542873\pi
198198 −8.81712 + 4.33630i −0.626605 + 0.308168i
199199 12.1254i 0.859544i 0.902937 + 0.429772i 0.141406π0.141406\pi
−0.902937 + 0.429772i 0.858594π0.858594\pi
200200 11.7676 7.80787i 0.832093 0.552100i
201201 0.414653 0.0292473
202202 3.21785 + 6.54293i 0.226407 + 0.460359i
203203 −3.23947 3.23947i −0.227366 0.227366i
204204 −3.06404 + 0.396665i −0.214526 + 0.0277721i
205205 0.145794 + 0.145794i 0.0101827 + 0.0101827i
206206 −6.07673 + 17.8382i −0.423386 + 1.24285i
207207 −6.22112 3.80380i −0.432398 0.264383i
208208 6.47467 + 3.77550i 0.448937 + 0.261784i
209209 −30.3513 −2.09945
210210 0.123623 0.362894i 0.00853078 0.0250421i
211211 8.84817 + 8.84817i 0.609133 + 0.609133i 0.942720 0.333586i 0.108259π-0.108259\pi
−0.333586 + 0.942720i 0.608259π0.608259\pi
212212 16.4115 2.12460i 1.12715 0.145918i
213213 −12.9130 12.9130i −0.884783 0.884783i
214214 −6.20412 12.6150i −0.424105 0.862344i
215215 0.974067 0.0664308
216216 −15.2434 3.08343i −1.03718 0.209801i
217217 −6.15748 −0.417997
218218 2.75964 + 5.61125i 0.186907 + 0.380042i
219219 1.89800 1.89800i 0.128255 0.128255i
220220 0.606664 + 0.467593i 0.0409013 + 0.0315251i
221221 1.68271 + 1.68271i 0.113191 + 0.113191i
222222 3.56420 + 1.21417i 0.239214 + 0.0814900i
223223 8.33600i 0.558220i 0.960259 + 0.279110i 0.0900394π0.0900394\pi
−0.960259 + 0.279110i 0.909961π0.909961\pi
224224 15.0048 + 1.06478i 1.00255 + 0.0711434i
225225 7.59161 0.506107
226226 −3.95354 + 11.6056i −0.262985 + 0.771993i
227227 −4.72544 + 4.72544i −0.313638 + 0.313638i −0.846317 0.532679i 0.821185π-0.821185\pi
0.532679 + 0.846317i 0.321185π0.321185\pi
228228 −12.7980 9.86419i −0.847568 0.653272i
229229 15.7355 15.7355i 1.03983 1.03983i 0.0406573 0.999173i 0.487055π-0.487055\pi
0.999173 0.0406573i 0.0129452π-0.0129452\pi
230230 −0.0520600 + 0.566040i −0.00343273 + 0.0373235i
231231 −14.7804 −0.972477
232232 4.77617 + 0.966119i 0.313571 + 0.0634288i
233233 5.06132i 0.331578i −0.986161 0.165789i 0.946983π-0.946983\pi
0.986161 0.165789i 0.0530171π-0.0530171\pi
234234 1.77811 + 3.61547i 0.116239 + 0.236351i
235235 −0.102513 0.102513i −0.00668720 0.00668720i
236236 28.6747 3.71218i 1.86657 0.241642i
237237 −5.93863 5.93863i −0.385756 0.385756i
238238 4.52095 + 1.54010i 0.293050 + 0.0998297i
239239 25.4452i 1.64591i 0.568105 + 0.822956i 0.307677π0.307677\pi
−0.568105 + 0.822956i 0.692323π0.692323\pi
240240 0.103839 + 0.394332i 0.00670280 + 0.0254540i
241241 7.67284i 0.494251i 0.968983 + 0.247126i 0.0794860π0.0794860\pi
−0.968983 + 0.247126i 0.920514π0.920514\pi
242242 4.50601 13.2274i 0.289657 0.850289i
243243 −9.83484 9.83484i −0.630905 0.630905i
244244 −3.33509 25.7619i −0.213508 1.64924i
245245 −0.00421837 + 0.00421837i −0.000269502 + 0.000269502i
246246 3.79750 1.86763i 0.242120 0.119076i
247247 12.4456i 0.791896i
248248 5.45738 3.62101i 0.346544 0.229934i
249249 11.9771 0.759017
250250 −0.522711 1.06284i −0.0330591 0.0672200i
251251 −18.0092 18.0092i −1.13673 1.13673i −0.989033 0.147695i 0.952814π-0.952814\pi
−0.147695 0.989033i 0.547186π-0.547186\pi
252252 6.40467 + 4.93646i 0.403456 + 0.310968i
253253 21.3043 5.13712i 1.33939 0.322968i
254254 −2.38108 + 6.98967i −0.149403 + 0.438571i
255255 0.129470i 0.00810776i
256256 −13.9249 + 7.88012i −0.870308 + 0.492508i
257257 −11.5321 −0.719351 −0.359675 0.933077i 0.617113π-0.617113\pi
−0.359675 + 0.933077i 0.617113π0.617113\pi
258258 6.44685 18.9247i 0.401363 1.17820i
259259 −4.11582 4.11582i −0.255745 0.255745i
260260 0.191737 0.248764i 0.0118910 0.0154277i
261261 1.85226 + 1.85226i 0.114652 + 0.114652i
262262 −2.94320 5.98448i −0.181831 0.369722i
263263 25.8401i 1.59337i −0.604396 0.796684i 0.706586π-0.706586\pi
0.604396 0.796684i 0.293414π-0.293414\pi
264264 13.0999 8.69185i 0.806240 0.534946i
265265 0.693464i 0.0425992i
266266 11.0235 + 22.4143i 0.675891 + 1.37431i
267267 −12.2658 12.2658i −0.750656 0.750656i
268268 0.676148 0.0875329i 0.0413023 0.00534692i
269269 12.0864 12.0864i 0.736922 0.736922i −0.235059 0.971981i 0.575528π-0.575528\pi
0.971981 + 0.235059i 0.0755284π0.0755284\pi
270270 −0.210153 + 0.616903i −0.0127895 + 0.0375435i
271271 19.6896i 1.19606i 0.801474 + 0.598030i 0.204050π0.204050\pi
−0.801474 + 0.598030i 0.795950π0.795950\pi
272272 −4.91260 + 1.29363i −0.297870 + 0.0784381i
273273 6.06071i 0.366811i
274274 9.93963 + 3.38601i 0.600475 + 0.204556i
275275 −16.1332 + 16.1332i −0.972867 + 0.972867i
276276 10.6528 + 4.75777i 0.641221 + 0.286384i
277277 −8.60109 8.60109i −0.516789 0.516789i 0.399809 0.916598i 0.369076π-0.369076\pi
−0.916598 + 0.399809i 0.869076π0.869076\pi
278278 −11.9562 + 5.88013i −0.717087 + 0.352667i
279279 3.52072 0.210780
280280 0.124977 0.617846i 0.00746881 0.0369233i
281281 −28.6536 −1.70933 −0.854665 0.519181i 0.826237π-0.826237\pi
−0.854665 + 0.519181i 0.826237π0.826237\pi
282282 −2.67015 + 1.31319i −0.159005 + 0.0781996i
283283 4.00191 + 4.00191i 0.237889 + 0.237889i 0.815976 0.578086i 0.196200π-0.196200\pi
−0.578086 + 0.815976i 0.696200π0.696200\pi
284284 −23.7823 18.3305i −1.41122 1.08771i
285285 −0.478793 + 0.478793i −0.0283612 + 0.0283612i
286286 −11.4621 3.90465i −0.677767 0.230887i
287287 −6.54190 −0.386156
288288 −8.57944 0.608817i −0.505548 0.0358749i
289289 15.3871 0.905121
290290 0.0658464 0.193292i 0.00386663 0.0113505i
291291 6.87660 6.87660i 0.403113 0.403113i
292292 2.69428 3.49562i 0.157671 0.204565i
293293 −9.94696 + 9.94696i −0.581107 + 0.581107i −0.935208 0.354100i 0.884787π-0.884787\pi
0.354100 + 0.935208i 0.384787π0.384787\pi
294294 0.0540376 + 0.109876i 0.00315154 + 0.00640810i
295295 1.21164i 0.0705447i
296296 6.06823 + 1.22748i 0.352709 + 0.0713456i
297297 25.1259 1.45795
298298 −11.8062 + 5.80633i −0.683912 + 0.336352i
299299 −2.10648 8.73586i −0.121821 0.505208i
300300 −12.0460 + 1.55946i −0.695478 + 0.0900353i
301301 −21.8536 + 21.8536i −1.25962 + 1.25962i
302302 −20.8909 7.11663i −1.20213 0.409516i
303303 6.27132i 0.360278i
304304 −22.9512 13.3833i −1.31634 0.767583i
305305 −1.08857 −0.0623311
306306 −2.58499 0.880596i −0.147774 0.0503403i
307307 10.7455 + 10.7455i 0.613280 + 0.613280i 0.943799 0.330519i 0.107224π-0.107224\pi
−0.330519 + 0.943799i 0.607224π0.607224\pi
308308 −24.1014 + 3.12012i −1.37331 + 0.177786i
309309 11.4611 11.4611i 0.652000 0.652000i
310310 −0.121122 0.246281i −0.00687927 0.0139878i
311311 14.1242 0.800908 0.400454 0.916317i 0.368852π-0.368852\pi
0.400454 + 0.916317i 0.368852π0.368852\pi
312312 −3.56411 5.37162i −0.201778 0.304108i
313313 24.3707 1.37751 0.688757 0.724992i 0.258157π-0.258157\pi
0.688757 + 0.724992i 0.258157π0.258157\pi
314314 −5.34499 10.8681i −0.301635 0.613323i
315315 0.239609 0.239609i 0.0135004 0.0135004i
316316 −10.9374 8.43011i −0.615277 0.474231i
317317 10.5047 10.5047i 0.590001 0.590001i −0.347630 0.937632i 0.613014π-0.613014\pi
0.937632 + 0.347630i 0.113014π0.113014\pi
318318 −13.4730 4.58968i −0.755529 0.257377i
319319 −7.87261 −0.440781
320320 0.252567 + 0.621092i 0.0141190 + 0.0347201i
321321 12.0913i 0.674873i
322322 −11.5313 13.8673i −0.642617 0.772795i
323323 −5.96482 5.96482i −0.331891 0.331891i
324324 3.36907 + 2.59674i 0.187170 + 0.144263i
325325 6.61544 + 6.61544i 0.366959 + 0.366959i
326326 9.52260 + 19.3626i 0.527408 + 1.07239i
327327 5.37833i 0.297422i
328328 5.79809 3.84708i 0.320146 0.212419i
329329 4.59983 0.253597
330330 −0.290741 0.591170i −0.0160047 0.0325429i
331331 −8.83567 + 8.83567i −0.485652 + 0.485652i −0.906931 0.421279i 0.861581π-0.861581\pi
0.421279 + 0.906931i 0.361581π0.361581\pi
332332 19.5303 2.52836i 1.07186 0.138762i
333333 2.35334 + 2.35334i 0.128962 + 0.128962i
334334 8.94177 + 3.04608i 0.489272 + 0.166674i
335335 0.0285705i 0.00156097i
336336 −11.1767 6.51732i −0.609738 0.355549i
337337 10.6494i 0.580110i −0.957010 0.290055i 0.906326π-0.906326\pi
0.957010 0.290055i 0.0936735π-0.0936735\pi
338338 4.32726 12.7027i 0.235372 0.690934i
339339 7.45663 7.45663i 0.404989 0.404989i
340340 0.0273311 + 0.211119i 0.00148224 + 0.0114496i
341341 −7.48199 + 7.48199i −0.405173 + 0.405173i
342342 −6.30298 12.8160i −0.340826 0.693011i
343343 18.4249i 0.994851i
344344 6.51748 32.2203i 0.351399 1.73720i
345345 0.255038 0.417114i 0.0137308 0.0224567i
346346 −16.3481 + 8.04009i −0.878880 + 0.432238i
347347 −16.4276 + 16.4276i −0.881879 + 0.881879i −0.993725 0.111847i 0.964323π-0.964323\pi
0.111847 + 0.993725i 0.464323π0.464323\pi
348348 −3.31958 2.55860i −0.177948 0.137155i
349349 −5.53040 + 5.53040i −0.296036 + 0.296036i −0.839459 0.543423i 0.817128π-0.817128\pi
0.543423 + 0.839459i 0.317128π0.317128\pi
350350 17.7737 + 6.05477i 0.950047 + 0.323641i
351351 10.3029i 0.549929i
352352 19.5263 16.9386i 1.04075 0.902832i
353353 32.2050 1.71410 0.857050 0.515233i 0.172295π-0.172295\pi
0.857050 + 0.515233i 0.172295π0.172295\pi
354354 −23.5405 8.01925i −1.25116 0.426218i
355355 −0.889733 + 0.889733i −0.0472221 + 0.0472221i
356356 −22.5904 17.4118i −1.19729 0.922823i
357357 −2.90472 2.90472i −0.153734 0.153734i
358358 −0.0802949 0.163266i −0.00424372 0.00862886i
359359 13.6769i 0.721838i 0.932597 + 0.360919i 0.117537π0.117537\pi
−0.932597 + 0.360919i 0.882463π0.882463\pi
360360 −0.0714593 + 0.353271i −0.00376624 + 0.0186190i
361361 25.1168i 1.32194i
362362 −20.3106 + 9.98887i −1.06750 + 0.525004i
363363 −8.49863 + 8.49863i −0.446063 + 0.446063i
364364 1.27941 + 9.88282i 0.0670594 + 0.518001i
365365 −0.130776 0.130776i −0.00684515 0.00684515i
366366 −7.20466 + 21.1492i −0.376593 + 1.10549i
367367 −18.4813 −0.964716 −0.482358 0.875974i 0.660220π-0.660220\pi
−0.482358 + 0.875974i 0.660220π0.660220\pi
368368 18.3752 + 5.50941i 0.957871 + 0.287198i
369369 3.74052 0.194724
370370 0.0836593 0.245582i 0.00434924 0.0127672i
371371 15.5582 + 15.5582i 0.807739 + 0.807739i
372372 −5.58652 + 0.723221i −0.289648 + 0.0374973i
373373 −2.68817 + 2.68817i −0.139188 + 0.139188i −0.773268 0.634080i 0.781379π-0.781379\pi
0.634080 + 0.773268i 0.281379π0.281379\pi
374374 7.36482 3.62206i 0.380826 0.187292i
375375 1.01872i 0.0526065i
376376 −4.07684 + 2.70501i −0.210247 + 0.139500i
377377 3.22818i 0.166260i
378378 −9.12560 18.5553i −0.469370 0.954383i
379379 17.1581 + 17.1581i 0.881353 + 0.881353i 0.993672 0.112319i 0.0358279π-0.0358279\pi
−0.112319 + 0.993672i 0.535828π0.535828\pi
380380 −0.679665 + 0.881810i −0.0348661 + 0.0452359i
381381 4.49088 4.49088i 0.230075 0.230075i
382382 21.0899 + 7.18442i 1.07905 + 0.367587i
383383 9.20129 0.470164 0.235082 0.971976i 0.424464π-0.424464\pi
0.235082 + 0.971976i 0.424464π0.424464\pi
384384 13.7385 0.796331i 0.701091 0.0406376i
385385 1.01840i 0.0519025i
386386 13.3195 + 4.53739i 0.677944 + 0.230947i
387387 12.4954 12.4954i 0.635179 0.635179i
388388 9.76159 12.6649i 0.495569 0.642962i
389389 −19.1433 + 19.1433i −0.970606 + 0.970606i −0.999580 0.0289741i 0.990776π-0.990776\pi
0.0289741 + 0.999580i 0.490776π0.490776\pi
390390 −0.242410 + 0.119219i −0.0122749 + 0.00603687i
391391 5.19642 + 3.17727i 0.262794 + 0.160681i
392392 0.111310 + 0.167761i 0.00562203 + 0.00847319i
393393 5.73606i 0.289346i
394394 −10.6127 21.5791i −0.534661 1.08714i
395395 −0.409185 + 0.409185i −0.0205883 + 0.0205883i
396396 13.7807 1.78402i 0.692506 0.0896505i
397397 4.43182 4.43182i 0.222426 0.222426i −0.587093 0.809519i 0.699728π-0.699728\pi
0.809519 + 0.587093i 0.199728π0.199728\pi
398398 5.52951 16.2319i 0.277169 0.813630i
399399 21.4838i 1.07554i
400400 −19.3135 + 5.08582i −0.965675 + 0.254291i
401401 9.14611i 0.456735i 0.973575 + 0.228367i 0.0733388π0.0733388\pi
−0.973575 + 0.228367i 0.926661π0.926661\pi
402402 −0.555083 0.189093i −0.0276850 0.00943112i
403403 3.06801 + 3.06801i 0.152828 + 0.152828i
404404 −1.32387 10.2263i −0.0658651 0.508775i
405405 0.126042 0.126042i 0.00626308 0.00626308i
406406 2.85929 + 5.81387i 0.141904 + 0.288538i
407407 −10.0023 −0.495797
408408 4.28263 + 0.866286i 0.212022 + 0.0428876i
409409 38.6304i 1.91015i −0.296365 0.955075i 0.595775π-0.595775\pi
0.296365 0.955075i 0.404225π-0.404225\pi
410410 −0.128684 0.261656i −0.00635525 0.0129223i
411411 −6.38624 6.38624i −0.315010 0.315010i
412412 16.2695 21.1083i 0.801540 1.03993i
413413 27.1837 + 27.1837i 1.33762 + 1.33762i
414414 6.59338 + 7.92905i 0.324047 + 0.389691i
415415 0.825248i 0.0405098i
416416 −6.94571 8.00678i −0.340542 0.392565i
417417 11.4599 0.561194
418418 40.6304 + 13.8411i 1.98730 + 0.676989i
419419 −12.1063 + 12.1063i −0.591429 + 0.591429i −0.938017 0.346588i 0.887340π-0.887340\pi
0.346588 + 0.938017i 0.387340π0.387340\pi
420420 −0.330980 + 0.429420i −0.0161502 + 0.0209536i
421421 −13.6001 + 13.6001i −0.662827 + 0.662827i −0.956045 0.293219i 0.905274π-0.905274\pi
0.293219 + 0.956045i 0.405274π0.405274\pi
422422 −7.80977 15.8798i −0.380174 0.773017i
423423 −2.63009 −0.127879
424424 −22.9385 4.63996i −1.11399 0.225337i
425425 −6.34117 −0.307592
426426 11.3975 + 23.1749i 0.552213 + 1.12283i
427427 24.4224 24.4224i 1.18188 1.18188i
428428 2.55247 + 19.7166i 0.123378 + 0.953037i
429429 7.36442 + 7.36442i 0.355557 + 0.355557i
430430 −1.30396 0.444202i −0.0628823 0.0214213i
431431 −6.75253 −0.325258 −0.162629 0.986687i 0.551997π-0.551997\pi
−0.162629 + 0.986687i 0.551997π0.551997\pi
432432 18.9998 + 11.0791i 0.914129 + 0.533045i
433433 8.63103i 0.414781i −0.978258 0.207390i 0.933503π-0.933503\pi
0.978258 0.207390i 0.0664970π-0.0664970\pi
434434 8.24283 + 2.80798i 0.395669 + 0.134788i
435435 −0.124191 + 0.124191i −0.00595448 + 0.00595448i
436436 −1.13536 8.77010i −0.0543739 0.420011i
437437 7.46700 + 30.9666i 0.357195 + 1.48133i
438438 −3.40634 + 1.67525i −0.162761 + 0.0800467i
439439 −23.6988 −1.13108 −0.565540 0.824721i 0.691332π-0.691332\pi
−0.565540 + 0.824721i 0.691332π0.691332\pi
440440 −0.598888 0.902609i −0.0285509 0.0430302i
441441 0.108227i 0.00515369i
442442 −1.48523 3.01996i −0.0706452 0.143645i
443443 −16.5520 + 16.5520i −0.786407 + 0.786407i −0.980903 0.194496i 0.937693π-0.937693\pi
0.194496 + 0.980903i 0.437693π0.437693\pi
444444 −4.21760 3.25076i −0.200158 0.154274i
445445 −0.845142 + 0.845142i −0.0400636 + 0.0400636i
446446 3.80145 11.1592i 0.180004 0.528401i
447447 11.3161 0.535232
448448 −19.6009 8.26800i −0.926056 0.390626i
449449 −22.5417 −1.06381 −0.531904 0.846804i 0.678523π-0.678523\pi
−0.531904 + 0.846804i 0.678523π0.678523\pi
450450 −10.1627 3.46199i −0.479073 0.163200i
451451 −7.94911 + 7.94911i −0.374309 + 0.374309i
452452 10.5850 13.7331i 0.497875 0.645953i
453453 13.4224 + 13.4224i 0.630641 + 0.630641i
454454 8.48073 4.17087i 0.398021 0.195749i
455455 0.417597 0.0195772
456456 12.6339 + 19.0411i 0.591639 + 0.891683i
457457 19.8676 0.929365 0.464683 0.885477i 0.346168π-0.346168\pi
0.464683 + 0.885477i 0.346168π0.346168\pi
458458 −28.2405 + 13.8888i −1.31959 + 0.648981i
459459 4.93789 + 4.93789i 0.230481 + 0.230481i
460460 0.327821 0.733999i 0.0152847 0.0342229i
461461 −28.8571 + 28.8571i −1.34401 + 1.34401i −0.451982 + 0.892027i 0.649283π0.649283\pi
−0.892027 + 0.451982i 0.850717π0.850717\pi
462462 19.7860 + 6.74027i 0.920530 + 0.313586i
463463 23.6252i 1.09796i −0.835837 0.548978i 0.815017π-0.815017\pi
0.835837 0.548978i 0.184983π-0.184983\pi
464464 −5.95314 3.47139i −0.276368 0.161155i
465465 0.236057i 0.0109469i
466466 −2.30810 + 6.77544i −0.106921 + 0.313866i
467467 −2.66814 + 2.66814i −0.123467 + 0.123467i −0.766140 0.642674i 0.777825π-0.777825\pi
0.642674 + 0.766140i 0.277825π0.277825\pi
468468 −0.731542 5.65080i −0.0338155 0.261208i
469469 0.640991 + 0.640991i 0.0295982 + 0.0295982i
470470 0.0904821 + 0.183980i 0.00417363 + 0.00848634i
471471 10.4170i 0.479988i
472472 −40.0789 8.10711i −1.84478 0.373160i
473473 53.1089i 2.44195i
474474 5.24169 + 10.6581i 0.240759 + 0.489541i
475475 −23.4502 23.4502i −1.07597 1.07597i
476476 −5.34973 4.12336i −0.245205 0.188994i
477477 −8.89583 8.89583i −0.407312 0.407312i
478478 11.6037 34.0627i 0.530742 1.55799i
479479 13.6769 0.624914 0.312457 0.949932i 0.398848π-0.398848\pi
0.312457 + 0.949932i 0.398848π0.398848\pi
480480 0.0408200 0.575234i 0.00186317 0.0262557i
481481 4.10147i 0.187011i
482482 3.49903 10.2714i 0.159377 0.467850i
483483 3.63625 + 15.0800i 0.165455 + 0.686163i
484484 −12.0641 + 15.6522i −0.548369 + 0.711465i
485485 −0.473813 0.473813i −0.0215147 0.0215147i
486486 8.68064 + 17.6506i 0.393762 + 0.800646i
487487 15.9805 0.724144 0.362072 0.932150i 0.382069π-0.382069\pi
0.362072 + 0.932150i 0.382069π0.382069\pi
488488 −7.28359 + 36.0076i −0.329712 + 1.62999i
489489 18.5588i 0.839258i
490490 0.00757071 0.00372331i 0.000342010 0.000168202i
491491 23.4883 23.4883i 1.06001 1.06001i 0.0619296 0.998081i 0.480275π-0.480275\pi
0.998081 0.0619296i 0.0197254π-0.0197254\pi
492492 −5.93530 + 0.768373i −0.267584 + 0.0346409i
493493 −1.54717 1.54717i −0.0696811 0.0696811i
494494 5.67555 16.6606i 0.255355 0.749595i
495495 0.582300i 0.0261724i
496496 −8.95691 + 2.35862i −0.402177 + 0.105905i
497497 39.9231i 1.79079i
498498 −16.0334 5.46189i −0.718473 0.244753i
499499 25.4995 + 25.4995i 1.14152 + 1.14152i 0.988173 + 0.153343i 0.0490039π0.0490039\pi
0.153343 + 0.988173i 0.450996π0.450996\pi
500500 0.215051 + 1.66116i 0.00961739 + 0.0742895i
501501 −5.74511 5.74511i −0.256673 0.256673i
502502 15.8956 + 32.3210i 0.709457 + 1.44256i
503503 19.6250i 0.875035i −0.899210 0.437517i 0.855858π-0.855858\pi
0.899210 0.437517i 0.144142π-0.144142\pi
504504 −6.32257 9.52901i −0.281630 0.424456i
505505 −0.432108 −0.0192286
506506 −30.8621 2.83846i −1.37199 0.126185i
507507 −8.16150 + 8.16150i −0.362465 + 0.362465i
508508 6.37497 8.27102i 0.282844 0.366967i
509509 12.6219 12.6219i 0.559456 0.559456i −0.369697 0.929153i 0.620538π-0.620538\pi
0.929153 + 0.369697i 0.120538π0.120538\pi
510510 0.0590422 0.173318i 0.00261443 0.00767466i
511511 5.86805 0.259587
512512 22.2344 4.19872i 0.982633 0.185559i
513513 36.5215i 1.61246i
514514 15.4376 + 5.25895i 0.680925 + 0.231962i
515515 −0.789696 0.789696i −0.0347982 0.0347982i
516516 −17.2604 + 22.3940i −0.759847 + 0.985841i
517517 5.58929 5.58929i 0.245817 0.245817i
518518 3.63279 + 7.38666i 0.159616 + 0.324551i
519519 15.6695 0.687814
520520 −0.370116 + 0.245575i −0.0162307 + 0.0107692i
521521 12.0617 0.528434 0.264217 0.964463i 0.414886π-0.414886\pi
0.264217 + 0.964463i 0.414886π0.414886\pi
522522 −1.63488 3.32425i −0.0715570 0.145499i
523523 −1.82928 1.82928i −0.0799888 0.0799888i 0.665980 0.745969i 0.268013π-0.268013\pi
−0.745969 + 0.665980i 0.768013π0.768013\pi
524524 1.21088 + 9.35343i 0.0528974 + 0.408606i
525525 −11.4197 11.4197i −0.498396 0.498396i
526526 −11.7838 + 34.5914i −0.513799 + 1.50825i
527527 −2.94081 −0.128104
528528 −21.5001 + 5.66162i −0.935672 + 0.246390i
529529 −10.4825 20.4723i −0.455761 0.890102i
530530 −0.316239 + 0.928320i −0.0137366 + 0.0403236i
531531 −15.5431 15.5431i −0.674513 0.674513i
532532 −4.53522 35.0323i −0.196627 1.51884i
533533 3.25955 + 3.25955i 0.141187 + 0.141187i
534534 10.8263 + 22.0134i 0.468501 + 0.952615i
535535 0.833120 0.0360189
536536 −0.945057 0.191165i −0.0408202 0.00825707i
537537 0.156488i 0.00675297i
538538 −21.6915 + 10.6680i −0.935186 + 0.459929i
539539 −0.229998 0.229998i −0.00990670 0.00990670i
540540 0.562650 0.729994i 0.0242126 0.0314139i
541541 −1.64738 + 1.64738i −0.0708265 + 0.0708265i −0.741633 0.670806i 0.765948π-0.765948\pi
0.670806 + 0.741633i 0.265948π0.265948\pi
542542 8.97903 26.3579i 0.385682 1.13217i
543543 19.4675 0.835431
544544 7.16629 + 0.508537i 0.307252 + 0.0218034i
545545 −0.370579 −0.0158738
546546 2.76386 8.11330i 0.118282 0.347217i
547547 −18.0346 18.0346i −0.771105 0.771105i 0.207195 0.978300i 0.433567π-0.433567\pi
−0.978300 + 0.207195i 0.933567π0.933567\pi
548548 −11.7618 9.06551i −0.502438 0.387259i
549549 −13.9642 + 13.9642i −0.595979 + 0.595979i
550550 28.9542 14.2398i 1.23461 0.607188i
551551 11.4431i 0.487494i
552552 −12.0909 11.2271i −0.514621 0.477855i
553553 18.3605i 0.780767i
554554 7.59168 + 15.4364i 0.322540 + 0.655828i
555555 −0.157787 + 0.157787i −0.00669768 + 0.00669768i
556556 18.6869 2.41918i 0.792503 0.102596i
557557 −14.7445 14.7445i −0.624743 0.624743i 0.321997 0.946741i 0.395646π-0.395646\pi
−0.946741 + 0.321997i 0.895646π0.895646\pi
558558 −4.71308 1.60555i −0.199521 0.0679683i
559559 21.7774 0.921086
560560 −0.449058 + 0.770098i −0.0189762 + 0.0325426i
561561 −7.05910 −0.298035
562562 38.3577 + 13.0668i 1.61802 + 0.551192i
563563 −7.74891 + 7.74891i −0.326578 + 0.326578i −0.851284 0.524706i 0.824175π-0.824175\pi
0.524706 + 0.851284i 0.324175π0.324175\pi
564564 4.17331 0.540269i 0.175728 0.0227494i
565565 −0.513779 0.513779i −0.0216148 0.0216148i
566566 −3.53226 7.18223i −0.148472 0.301892i
567567 5.65561i 0.237513i
568568 23.4775 + 35.3839i 0.985092 + 1.48467i
569569 3.63750 0.152492 0.0762460 0.997089i 0.475707π-0.475707\pi
0.0762460 + 0.997089i 0.475707π0.475707\pi
570570 0.859289 0.422603i 0.0359917 0.0177009i
571571 −12.0122 12.0122i −0.502695 0.502695i 0.409579 0.912275i 0.365676π-0.365676\pi
−0.912275 + 0.409579i 0.865676π0.865676\pi
572572 13.5633 + 10.4541i 0.567111 + 0.437106i
573573 −13.5503 13.5503i −0.566072 0.566072i
574574 8.75745 + 2.98329i 0.365529 + 0.124520i
575575 20.4293 + 12.4912i 0.851961 + 0.520918i
576576 11.2074 + 4.72747i 0.466975 + 0.196978i
577577 −20.4216 −0.850164 −0.425082 0.905155i 0.639755π-0.639755\pi
−0.425082 + 0.905155i 0.639755π0.639755\pi
578578 −20.5982 7.01693i −0.856772 0.291866i
579579 −8.55781 8.55781i −0.355650 0.355650i
580580 −0.176293 + 0.228726i −0.00732018 + 0.00949734i
581581 18.5148 + 18.5148i 0.768123 + 0.768123i
582582 −12.3414 + 6.06957i −0.511568 + 0.251592i
583583 37.8097 1.56592
584584 −5.20086 + 3.45081i −0.215213 + 0.142795i
585585 −0.238773 −0.00987206
586586 17.8518 8.77960i 0.737451 0.362682i
587587 −17.0110 + 17.0110i −0.702118 + 0.702118i −0.964865 0.262747i 0.915372π-0.915372\pi
0.262747 + 0.964865i 0.415372π0.415372\pi
588588 −0.0222319 0.171731i −0.000916829 0.00708205i
589589 −10.8754 10.8754i −0.448112 0.448112i
590590 −0.552544 + 1.62199i −0.0227479 + 0.0667764i
591591 20.6833i 0.850799i
592592 −7.56360 4.41047i −0.310862 0.181269i
593593 −3.97528 −0.163245 −0.0816226 0.996663i 0.526010π-0.526010\pi
−0.0816226 + 0.996663i 0.526010π0.526010\pi
594594 −33.6353 11.4581i −1.38007 0.470133i
595595 −0.200142 + 0.200142i −0.00820502 + 0.00820502i
596596 18.4524 2.38881i 0.755840 0.0978497i
597597 −10.4290 + 10.4290i −0.426831 + 0.426831i
598598 −1.16391 + 12.6551i −0.0475960 + 0.517504i
599599 −22.1613 −0.905487 −0.452744 0.891641i 0.649555π-0.649555\pi
−0.452744 + 0.891641i 0.649555π0.649555\pi
600600 16.8368 + 3.40573i 0.687360 + 0.139038i
601601 16.7533i 0.683381i −0.939813 0.341690i 0.889001π-0.889001\pi
0.939813 0.341690i 0.110999π-0.110999\pi
602602 39.2206 19.2889i 1.59851 0.786157i
603603 −0.366505 0.366505i −0.0149253 0.0149253i
604604 24.7206 + 19.0537i 1.00587 + 0.775282i
605605 0.585575 + 0.585575i 0.0238070 + 0.0238070i
606606 −2.85990 + 8.39524i −0.116176 + 0.341033i
607607 36.1916i 1.46897i 0.678624 + 0.734486i 0.262577π0.262577\pi
−0.678624 + 0.734486i 0.737423π0.737423\pi
608608 24.6209 + 28.3822i 0.998511 + 1.15105i
609609 5.57253i 0.225810i
610610 1.45723 + 0.496417i 0.0590015 + 0.0200993i
611611 −2.29190 2.29190i −0.0927203 0.0927203i
612612 3.05887 + 2.35765i 0.123647 + 0.0953025i
613613 −30.4776 + 30.4776i −1.23098 + 1.23098i −0.267392 + 0.963588i 0.586162π0.586162\pi
−0.963588 + 0.267392i 0.913838π0.913838\pi
614614 −9.48446 19.2850i −0.382762 0.778279i
615615 0.250795i 0.0101130i
616616 33.6867 + 6.81411i 1.35728 + 0.274548i
617617 −16.7959 −0.676176 −0.338088 0.941114i 0.609780π-0.609780\pi
−0.338088 + 0.941114i 0.609780π0.609780\pi
618618 −20.5692 + 10.1161i −0.827416 + 0.406928i
619619 10.5813 + 10.5813i 0.425300 + 0.425300i 0.887024 0.461724i 0.152769π-0.152769\pi
−0.461724 + 0.887024i 0.652769π0.652769\pi
620620 0.0498315 + 0.384924i 0.00200128 + 0.0154589i
621621 −6.18144 25.6353i −0.248053 1.02871i
622622 −18.9076 6.44102i −0.758126 0.258261i
623623 37.9222i 1.51932i
624624 2.32156 + 8.81616i 0.0929366 + 0.352929i
625625 −24.8947 −0.995787
626626 −32.6244 11.1137i −1.30393 0.444194i
627627 −26.1052 26.1052i −1.04254 1.04254i
628628 2.19901 + 16.9863i 0.0877502 + 0.677826i
629629 −1.96571 1.96571i −0.0783782 0.0783782i
630630 −0.430025 + 0.211489i −0.0171326 + 0.00842591i
631631 44.3752i 1.76655i 0.468857 + 0.883274i 0.344666π0.344666\pi
−0.468857 + 0.883274i 0.655334π0.655334\pi
632632 10.7972 + 16.2729i 0.429489 + 0.647301i
633633 15.2206i 0.604965i
634634 −18.8527 + 9.27187i −0.748737 + 0.368233i
635635 −0.309432 0.309432i −0.0122794 0.0122794i
636636 15.9429 + 12.2881i 0.632176 + 0.487257i
637637 −0.0943110 + 0.0943110i −0.00373674 + 0.00373674i
638638 10.5388 + 3.59013i 0.417236 + 0.142135i
639639 22.8272i 0.903029i
640640 −0.0548690 0.946615i −0.00216889 0.0374183i
641641 22.6166i 0.893303i −0.894708 0.446652i 0.852616π-0.852616\pi
0.894708 0.446652i 0.147384π-0.147384\pi
642642 5.51399 16.1863i 0.217620 0.638823i
643643 25.9171 25.9171i 1.02207 1.02207i 0.0223210 0.999751i 0.492894π-0.492894\pi
0.999751 0.0223210i 0.00710559π-0.00710559\pi
644644 9.11278 + 23.8224i 0.359094 + 0.938733i
645645 0.837795 + 0.837795i 0.0329881 + 0.0329881i
646646 5.26480 + 10.7051i 0.207141 + 0.421185i
647647 −16.0802 −0.632179 −0.316090 0.948729i 0.602370π-0.602370\pi
−0.316090 + 0.948729i 0.602370π0.602370\pi
648648 −3.32588 5.01257i −0.130653 0.196912i
649649 66.0623 2.59317
650650 −5.83906 11.8727i −0.229027 0.465686i
651651 −5.29604 5.29604i −0.207568 0.207568i
652652 −3.91775 30.2627i −0.153431 1.18518i
653653 25.6456 25.6456i 1.00359 1.00359i 0.00359817 0.999994i 0.498855π-0.498855\pi
0.999994 0.00359817i 0.00114534π-0.00114534\pi
654654 −2.45267 + 7.19980i −0.0959070 + 0.281535i
655655 0.395227 0.0154428
656656 −9.51611 + 2.50587i −0.371542 + 0.0978380i
657657 −3.35523 −0.130900
658658 −6.15766 2.09765i −0.240051 0.0817751i
659659 −5.67720 + 5.67720i −0.221152 + 0.221152i −0.808984 0.587831i 0.799982π-0.799982\pi
0.587831 + 0.808984i 0.299982π0.299982\pi
660660 0.119615 + 0.923968i 0.00465602 + 0.0359654i
661661 25.6539 25.6539i 0.997820 0.997820i −0.00217783 0.999998i 0.500693π-0.500693\pi
0.999998 + 0.00217783i 0.000693226π0.000693226\pi
662662 15.8574 7.79873i 0.616314 0.303106i
663663 2.89460i 0.112417i
664664 −27.2976 5.52173i −1.05935 0.214285i
665665 −1.48028 −0.0574030
666666 −2.07716 4.22354i −0.0804882 0.163659i
667667 1.93681 + 8.03220i 0.0749936 + 0.311008i
668668 −10.5810 8.15540i −0.409390 0.315542i
669669 −7.16979 + 7.16979i −0.277200 + 0.277200i
670670 −0.0130290 + 0.0382465i −0.000503353 + 0.00147759i
671671 59.3517i 2.29125i
672672 11.9898 + 13.8214i 0.462517 + 0.533173i
673673 −14.3871 −0.554583 −0.277291 0.960786i 0.589437π-0.589437\pi
−0.277291 + 0.960786i 0.589437π0.589437\pi
674674 −4.85643 + 14.2560i −0.187063 + 0.549122i
675675 19.4129 + 19.4129i 0.747203 + 0.747203i
676676 −11.5856 + 15.0313i −0.445598 + 0.578128i
677677 −9.48874 + 9.48874i −0.364682 + 0.364682i −0.865533 0.500851i 0.833020π-0.833020\pi
0.500851 + 0.865533i 0.333020π0.333020\pi
678678 −13.3824 + 6.58154i −0.513948 + 0.252762i
679679 21.2604 0.815898
680680 0.0596890 0.295083i 0.00228897 0.0113159i
681681 −8.12869 −0.311492
682682 13.4279 6.60392i 0.514182 0.252877i
683683 −10.0685 + 10.0685i −0.385260 + 0.385260i −0.872993 0.487733i 0.837824π-0.837824\pi
0.487733 + 0.872993i 0.337824π0.337824\pi
684684 2.59315 + 20.0308i 0.0991514 + 0.765895i
685685 −0.440026 + 0.440026i −0.0168125 + 0.0168125i
686686 8.40228 24.6649i 0.320801 0.941709i
687687 27.0682 1.03272
688688 −23.4181 + 40.1602i −0.892807 + 1.53109i
689689 15.5039i 0.590652i
690690 −0.531627 + 0.442074i −0.0202387 + 0.0168295i
691691 −25.0974 25.0974i −0.954750 0.954750i 0.0442700 0.999020i 0.485904π-0.485904\pi
−0.999020 + 0.0442700i 0.985904π0.985904\pi
692692 25.5512 3.30782i 0.971312 0.125744i
693693 13.0641 + 13.0641i 0.496266 + 0.496266i
694694 29.4826 14.4997i 1.11914 0.550400i
695695 0.789613i 0.0299517i
696696 3.27703 + 4.93894i 0.124215 + 0.187210i
697697 −3.12441 −0.118346
698698 9.92540 4.88136i 0.375682 0.184762i
699699 4.35324 4.35324i 0.164655 0.164655i
700700 −21.0320 16.2107i −0.794937 0.612706i
701701 1.25488 + 1.25488i 0.0473963 + 0.0473963i 0.730408 0.683011i 0.239330π-0.239330\pi
−0.683011 + 0.730408i 0.739330π0.739330\pi
702702 −4.69842 + 13.7922i −0.177331 + 0.520553i
703703 14.5388i 0.548340i
704704 −33.8637 + 13.7707i −1.27629 + 0.519003i
705705 0.176342i 0.00664144i
706706 −43.1119 14.6864i −1.62254 0.552730i
707707 9.69453 9.69453i 0.364600 0.364600i
708708 27.8559 + 21.4703i 1.04689 + 0.806902i
709709 17.0708 17.0708i 0.641106 0.641106i −0.309721 0.950827i 0.600236π-0.600236\pi
0.950827 + 0.309721i 0.100236π0.100236\pi
710710 1.59680 0.785316i 0.0599270 0.0294724i
711711 10.4981i 0.393711i
712712 22.3008 + 33.6105i 0.835758 + 1.25961i
713713 9.47438 + 5.79296i 0.354818 + 0.216948i
714714 2.56383 + 5.21310i 0.0959489 + 0.195095i
715715 0.507425 0.507425i 0.0189766 0.0189766i
716716 0.0330346 + 0.255176i 0.00123456 + 0.00953636i
717717 −21.8854 + 21.8854i −0.817325 + 0.817325i
718718 6.23705 18.3088i 0.232765 0.683280i
719719 10.8401i 0.404268i 0.979358 + 0.202134i 0.0647876π0.0647876\pi
−0.979358 + 0.202134i 0.935212π0.935212\pi
720720 0.256762 0.440326i 0.00956896 0.0164100i
721721 35.4343 1.31964
722722 −11.4540 + 33.6232i −0.426273 + 1.25132i
723723 −6.59940 + 6.59940i −0.245434 + 0.245434i
724724 31.7445 4.10958i 1.17977 0.152731i
725725 −6.08258 6.08258i −0.225901 0.225901i
726726 15.2525 7.50125i 0.566073 0.278397i
727727 10.3403i 0.383501i 0.981444 + 0.191751i 0.0614165π0.0614165\pi
−0.981444 + 0.191751i 0.938583π0.938583\pi
728728 2.79414 13.8133i 0.103558 0.511955i
729729 23.2984i 0.862903i
730730 0.115429 + 0.234704i 0.00427221 + 0.00868680i
731731 −10.4373 + 10.4373i −0.386037 + 0.386037i
732732 19.2893 25.0263i 0.712954 0.925000i
733733 18.2971 + 18.2971i 0.675819 + 0.675819i 0.959051 0.283232i 0.0914068π-0.0914068\pi
−0.283232 + 0.959051i 0.591407π0.591407\pi
734734 24.7404 + 8.42800i 0.913184 + 0.311083i
735735 −0.00725644 −0.000267658
736736 −22.0858 15.7549i −0.814094 0.580732i
737737 1.55775 0.0573803
738738 −5.00733 1.70579i −0.184322 0.0627908i
739739 29.3914 + 29.3914i 1.08118 + 1.08118i 0.996400 + 0.0847802i 0.0270188π0.0270188\pi
0.0847802 + 0.996400i 0.472981π0.472981\pi
740740 −0.223984 + 0.290602i −0.00823383 + 0.0106827i
741741 −10.7045 + 10.7045i −0.393238 + 0.393238i
742742 −13.7323 27.9222i −0.504128 1.02506i
743743 15.4325i 0.566163i −0.959096 0.283081i 0.908643π-0.908643\pi
0.959096 0.283081i 0.0913566π-0.0913566\pi
744744 7.80832 + 1.57946i 0.286267 + 0.0579057i
745745 0.779703i 0.0285661i
746746 4.82445 2.37269i 0.176636 0.0868704i
747747 −10.5864 10.5864i −0.387335 0.387335i
748748 −11.5108 + 1.49017i −0.420878 + 0.0544861i
749749 −18.6914 + 18.6914i −0.682969 + 0.682969i
750750 0.464566 1.36373i 0.0169635 0.0497965i
751751 14.9635 0.546026 0.273013 0.962010i 0.411980π-0.411980\pi
0.273013 + 0.962010i 0.411980π0.411980\pi
752752 6.69110 1.76197i 0.243999 0.0642523i
753753 30.9793i 1.12895i
754754 1.47214 4.32146i 0.0536122 0.157378i
755755 0.924836 0.924836i 0.0336582 0.0336582i
756756 3.75442 + 29.0010i 0.136547 + 1.05476i
757757 11.8442 11.8442i 0.430485 0.430485i −0.458308 0.888793i 0.651544π-0.651544\pi
0.888793 + 0.458308i 0.151544π0.151544\pi
758758 −15.1445 30.7936i −0.550072 1.11848i
759759 22.7422 + 13.9054i 0.825491 + 0.504733i
760760 1.31198 0.870507i 0.0475904 0.0315766i
761761 0.408106i 0.0147938i −0.999973 0.00739692i 0.997645π-0.997645\pi
0.999973 0.00739692i 0.00235453π-0.00235453\pi
762762 −8.05978 + 3.96384i −0.291975 + 0.143595i
763763 8.31408 8.31408i 0.300990 0.300990i
764764 −24.9561 19.2351i −0.902879 0.695903i
765765 0.114437 0.114437i 0.00413748 0.00413748i
766766 −12.3175 4.19605i −0.445049 0.151610i
767767 27.0890i 0.978126i
768768 −18.7545 5.19914i −0.676745 0.187608i
769769 44.9499i 1.62093i −0.585784 0.810467i 0.699213π-0.699213\pi
0.585784 0.810467i 0.300787π-0.300787\pi
770770 0.464419 1.36330i 0.0167365 0.0491300i
771771 −9.91873 9.91873i −0.357214 0.357214i
772772 −15.7612 12.1481i −0.567259 0.437221i
773773 −28.2917 + 28.2917i −1.01758 + 1.01758i −0.0177385 + 0.999843i 0.505647π0.505647\pi
−0.999843 + 0.0177385i 0.994353π0.994353\pi
774774 −22.4255 + 11.0290i −0.806070 + 0.396429i
775775 −11.5616 −0.415303
776776 −18.8431 + 12.5025i −0.676427 + 0.448815i
777777 7.08003i 0.253995i
778778 34.3565 16.8967i 1.23174 0.605777i
779779 −11.5543 11.5543i −0.413977 0.413977i
780780 0.378875 0.0490484i 0.0135659 0.00175622i
781781 −48.5108 48.5108i −1.73585 1.73585i
782782 −5.50737 6.62303i −0.196943 0.236839i
783783 9.47304i 0.338539i
784784 −0.0725044 0.275337i −0.00258944 0.00983346i
785785 0.717752 0.0256177
786786 2.61581 7.67869i 0.0933027 0.273890i
787787 23.2407 23.2407i 0.828442 0.828442i −0.158859 0.987301i 0.550782π-0.550782\pi
0.987301 + 0.158859i 0.0507815π0.0507815\pi
788788 4.36624 + 33.7270i 0.155541 + 1.20148i
789789 22.2250 22.2250i 0.791232 0.791232i
790790 0.734364 0.361164i 0.0261275 0.0128496i
791791 23.0537 0.819694
792792 −19.2614 3.89617i −0.684423 0.138444i
793793 −24.3373 −0.864242
794794 −7.95377 + 3.91171i −0.282269 + 0.138821i
795795 0.596448 0.596448i 0.0211538 0.0211538i
796796 −14.8044 + 19.2075i −0.524728 + 0.680792i
797797 16.5321 + 16.5321i 0.585598 + 0.585598i 0.936436 0.350838i 0.114103π-0.114103\pi
−0.350838 + 0.936436i 0.614103π0.614103\pi
798798 −9.79724 + 28.7598i −0.346819 + 1.01808i
799799 2.19688 0.0777200
800800 28.1737 + 1.99927i 0.996090 + 0.0706850i
801801 21.6831i 0.766136i
802802 4.17089 12.2436i 0.147279 0.432337i
803803 7.13030 7.13030i 0.251623 0.251623i
804804 0.656841 + 0.506267i 0.0231650 + 0.0178547i
805805 1.03905 0.250546i 0.0366215 0.00883057i
806806 −2.70795 5.50614i −0.0953835 0.193946i
807807 20.7910 0.731879
808808 −2.89123 + 14.2933i −0.101713 + 0.502837i
809809 3.22326i 0.113324i −0.998393 0.0566618i 0.981954π-0.981954\pi
0.998393 0.0566618i 0.0180457π-0.0180457\pi
810810 −0.226207 + 0.111250i −0.00794812 + 0.00390892i
811811 −12.6982 + 12.6982i −0.445893 + 0.445893i −0.893987 0.448093i 0.852103π-0.852103\pi
0.448093 + 0.893987i 0.352103π0.352103\pi
812812 −1.17636 9.08678i −0.0412821 0.318883i
813813 −16.9350 + 16.9350i −0.593937 + 0.593937i
814814 13.3898 + 4.56134i 0.469313 + 0.159875i
815815 −1.27874 −0.0447924
816816 −5.33798 3.11267i −0.186867 0.108965i
817817 −77.1959 −2.70074
818818 −17.6165 + 51.7133i −0.615948 + 1.80811i
819819 5.35698 5.35698i 0.187188 0.187188i
820820 0.0529426 + 0.408955i 0.00184884 + 0.0142813i
821821 −24.5612 24.5612i −0.857192 0.857192i 0.133814 0.991006i 0.457277π-0.457277\pi
−0.991006 + 0.133814i 0.957277π0.957277\pi
822822 5.63676 + 11.4614i 0.196605 + 0.399761i
823823 −45.6245 −1.59037 −0.795185 0.606367i 0.792626π-0.792626\pi
−0.795185 + 0.606367i 0.792626π0.792626\pi
824824 −31.4055 + 20.8378i −1.09406 + 0.725918i
825825 −27.7523 −0.966210
826826 −23.9935 48.7866i −0.834841 1.69750i
827827 0.390922 + 0.390922i 0.0135937 + 0.0135937i 0.713871 0.700277i 0.246940π-0.246940\pi
−0.700277 + 0.713871i 0.746940π0.746940\pi
828828 −5.21050 13.6211i −0.181077 0.473368i
829829 −12.4079 + 12.4079i −0.430943 + 0.430943i −0.888949 0.458006i 0.848564π-0.848564\pi
0.458006 + 0.888949i 0.348564π0.348564\pi
830830 −0.376337 + 1.10474i −0.0130628 + 0.0383459i
831831 14.7956i 0.513253i
832832 5.64670 + 13.8859i 0.195764 + 0.481406i
833833 0.0904010i 0.00313221i
834834 −15.3410 5.22604i −0.531217 0.180963i
835835 −0.395851 + 0.395851i −0.0136990 + 0.0136990i
836836 −48.0788 37.0573i −1.66284 1.28165i
837837 9.00301 + 9.00301i 0.311190 + 0.311190i
838838 21.7271 10.6855i 0.750549 0.369124i
839839 2.88285i 0.0995269i −0.998761 0.0497635i 0.984153π-0.984153\pi
0.998761 0.0497635i 0.0158467π-0.0158467\pi
840840 0.638901 0.423916i 0.0220442 0.0146265i
841841 26.0318i 0.897650i
842842 24.4080 12.0040i 0.841156 0.413685i
843843 −24.6449 24.6449i −0.848816 0.848816i
844844 3.21306 + 24.8193i 0.110598 + 0.854315i
845845 0.562346 + 0.562346i 0.0193453 + 0.0193453i
846846 3.52082 + 1.19940i 0.121048 + 0.0412361i
847847 −26.2752 −0.902827
848848 28.5911 + 16.6720i 0.981821 + 0.572518i
849849 6.88409i 0.236261i
850850 8.48874 + 2.89176i 0.291161 + 0.0991864i
851851 2.46076 + 10.2051i 0.0843538 + 0.349826i
852852 −4.68913 36.2212i −0.160647 1.24092i
853853 −4.58595 4.58595i −0.157020 0.157020i 0.624225 0.781245i 0.285415π-0.285415\pi
−0.781245 + 0.624225i 0.785415π0.785415\pi
854854 −43.8309 + 21.5562i −1.49986 + 0.737640i
855855 0.846396 0.0289461
856856 5.57440 27.5580i 0.190529 0.941913i
857857 18.1650i 0.620506i 0.950654 + 0.310253i 0.100414π0.100414\pi
−0.950654 + 0.310253i 0.899586π0.899586\pi
858858 −6.50014 13.2169i −0.221911 0.451218i
859859 24.8997 24.8997i 0.849566 0.849566i −0.140513 0.990079i 0.544875π-0.544875\pi
0.990079 + 0.140513i 0.0448750π0.0448750\pi
860860 1.54300 + 1.18928i 0.0526158 + 0.0405542i
861861 −5.62669 5.62669i −0.191757 0.191757i
862862 9.03941 + 3.07934i 0.307883 + 0.104883i
863863 17.1216i 0.582825i −0.956598 0.291412i 0.905875π-0.905875\pi
0.956598 0.291412i 0.0941252π-0.0941252\pi
864864 −20.3821 23.4958i −0.693413 0.799342i
865865 1.07966i 0.0367096i
866866 −3.93599 + 11.5541i −0.133751 + 0.392624i
867867 13.2344 + 13.2344i 0.449464 + 0.449464i
868868 −9.75391 7.51793i −0.331069 0.255175i
869869 −22.3099 22.3099i −0.756813 0.756813i
870870 0.222885 0.109616i 0.00755650 0.00371632i
871871 0.638756i 0.0216434i
872872 −2.47954 + 12.2580i −0.0839678 + 0.415109i
873873 −12.1562 −0.411426
874874 4.12581 44.8593i 0.139558 1.51739i
875875 −1.57479 + 1.57479i −0.0532376 + 0.0532376i
876876 5.32393 0.689226i 0.179879 0.0232868i
877877 −15.2309 + 15.2309i −0.514312 + 0.514312i −0.915845 0.401532i 0.868478π-0.868478\pi
0.401532 + 0.915845i 0.368478π0.368478\pi
878878 31.7248 + 10.8073i 1.07066 + 0.364729i
879879 −17.1107 −0.577131
880880 0.390098 + 1.48141i 0.0131502 + 0.0499382i
881881 51.1387i 1.72291i −0.507837 0.861453i 0.669555π-0.669555\pi
0.507837 0.861453i 0.330445π-0.330445\pi
882882 0.0493548 0.144881i 0.00166186 0.00487839i
883883 −2.24931 2.24931i −0.0756953 0.0756953i 0.668245 0.743941i 0.267046π-0.267046\pi
−0.743941 + 0.668245i 0.767046π0.767046\pi
884884 0.611047 + 4.72004i 0.0205517 + 0.158752i
885885 1.04213 1.04213i 0.0350310 0.0350310i
886886 29.7058 14.6095i 0.997985 0.490814i
887887 41.9597 1.40887 0.704435 0.709769i 0.251201π-0.251201\pi
0.704435 + 0.709769i 0.251201π0.251201\pi
888888 4.16353 + 6.27504i 0.139719 + 0.210576i
889889 13.8845 0.465670
890890 1.51678 0.745958i 0.0508424 0.0250046i
891891 6.87217 + 6.87217i 0.230226 + 0.230226i
892892 −10.1778 + 13.2049i −0.340777 + 0.442131i
893893 8.12425 + 8.12425i 0.271868 + 0.271868i
894894 −15.1485 5.16045i −0.506641 0.172591i
895895 0.0107824 0.000360416
896896 22.4687 + 20.0067i 0.750627 + 0.668377i
897897 5.70192 9.32549i 0.190382 0.311369i
898898 30.1759 + 10.2797i 1.00698 + 0.343037i
899899 −2.82088 2.82088i −0.0940817 0.0940817i
900900 12.0257 + 9.26893i 0.400856 + 0.308964i
901901 7.43057 + 7.43057i 0.247548 + 0.247548i
902902 14.2663 7.01622i 0.475014 0.233614i
903903 −37.5925 −1.25100
904904 −20.4325 + 13.5571i −0.679574 + 0.450903i
905905 1.34136i 0.0445882i
906906 −11.8472 24.0892i −0.393597 0.800311i
907907 −6.73858 6.73858i −0.223751 0.223751i 0.586325 0.810076i 0.300574π-0.300574\pi
−0.810076 + 0.586325i 0.800574π0.800574\pi
908908 −13.2549 + 1.71596i −0.439881 + 0.0569462i
909909 −5.54313 + 5.54313i −0.183854 + 0.183854i
910910 −0.559024 0.190436i −0.0185315 0.00631289i
911911 58.1801 1.92759 0.963796 0.266642i 0.0859142π-0.0859142\pi
0.963796 + 0.266642i 0.0859142π0.0859142\pi
912912 −8.22938 31.2513i −0.272502 1.03483i
913913 44.9949 1.48911
914914 −26.5961 9.06017i −0.879721 0.299684i
915915 −0.936275 0.936275i −0.0309523 0.0309523i
916916 44.1384 5.71407i 1.45837 0.188798i
917917 −8.86708 + 8.86708i −0.292817 + 0.292817i
918918 −4.35839 8.86202i −0.143848 0.292490i
919919 45.9219i 1.51482i 0.652938 + 0.757411i 0.273536π0.273536\pi
−0.652938 + 0.757411i 0.726464π0.726464\pi
920920 −0.773569 + 0.833087i −0.0255038 + 0.0274661i
921921 18.4845i 0.609083i
922922 51.7898 25.4705i 1.70561 0.838826i
923923 −19.8919 + 19.8919i −0.654751 + 0.654751i
924924 −23.4132 18.0460i −0.770238 0.593669i
925925 −7.72805 7.72805i −0.254097 0.254097i
926926 −10.7738 + 31.6263i −0.354048 + 1.03931i
927927 −20.2606 −0.665446
928928 6.38625 + 7.36184i 0.209639 + 0.241664i
929929 18.0479 0.592132 0.296066 0.955167i 0.404325π-0.404325\pi
0.296066 + 0.955167i 0.404325π0.404325\pi
930930 0.107649 0.316003i 0.00352994 0.0103621i
931931 0.334311 0.334311i 0.0109566 0.0109566i
932932 6.17958 8.01751i 0.202419 0.262622i
933933 12.1482 + 12.1482i 0.397714 + 0.397714i
934934 4.78850 2.35501i 0.156685 0.0770583i
935935 0.486388i 0.0159066i
936936 −1.59763 + 7.89816i −0.0522202 + 0.258159i
937937 3.77047 0.123176 0.0615879 0.998102i 0.480384π-0.480384\pi
0.0615879 + 0.998102i 0.480384π0.480384\pi
938938 −0.565765 1.15039i −0.0184729 0.0375614i
939939 20.9612 + 20.9612i 0.684044 + 0.684044i
940940 −0.0372257 0.287550i −0.00121417 0.00937886i
941941 19.3322 + 19.3322i 0.630212 + 0.630212i 0.948121 0.317909i 0.102981π-0.102981\pi
−0.317909 + 0.948121i 0.602981π0.602981\pi
942942 4.75043 13.9449i 0.154777 0.454348i
943943 10.0659 + 6.15462i 0.327790 + 0.200422i
944944 49.9553 + 29.1298i 1.62591 + 0.948095i
945945 1.22543 0.0398633
946946 24.2192 71.0954i 0.787434 2.31151i
947947 0.659158 + 0.659158i 0.0214197 + 0.0214197i 0.717736 0.696316i 0.245179π-0.245179\pi
−0.696316 + 0.717736i 0.745179π0.745179\pi
948948 −2.15651 16.6580i −0.0700403 0.541026i
949949 −2.92379 2.92379i −0.0949104 0.0949104i
950950 20.6981 + 42.0861i 0.671536 + 1.36545i
951951 18.0701 0.585964
952952 5.28116 + 7.95946i 0.171163 + 0.257967i
953953 −26.8329 −0.869203 −0.434601 0.900623i 0.643111π-0.643111\pi
−0.434601 + 0.900623i 0.643111π0.643111\pi
954954 7.85183 + 15.9653i 0.254213 + 0.516897i
955955 −0.933645 + 0.933645i −0.0302121 + 0.0302121i
956956 −31.0671 + 40.3071i −1.00478 + 1.30362i
957957 −6.77123 6.77123i −0.218883 0.218883i
958958 −18.3089 6.23706i −0.591533 0.201510i
959959 19.7443i 0.637578i
960960 −0.316968 + 0.751434i −0.0102301 + 0.0242524i
961961 25.6382 0.827037
962962 1.87039 5.49052i 0.0603037 0.177021i
963963 10.6874 10.6874i 0.344395 0.344395i
964964 −9.36810 + 12.1544i −0.301726 + 0.391466i
965965 −0.589652 + 0.589652i −0.0189816 + 0.0189816i
966966 2.00917 21.8454i 0.0646439 0.702863i
967967 −15.2802 −0.491379 −0.245690 0.969349i 0.579014π-0.579014\pi
−0.245690 + 0.969349i 0.579014π0.579014\pi
968968 23.2878 15.4516i 0.748497 0.496633i
969969 10.2607i 0.329620i
970970 0.418207 + 0.850351i 0.0134278 + 0.0273031i
971971 −5.62452 5.62452i −0.180499 0.180499i 0.611074 0.791573i 0.290738π-0.290738\pi
−0.791573 + 0.611074i 0.790738π0.790738\pi
972972 −3.57135 27.5869i −0.114551 0.884851i
973973 17.7153 + 17.7153i 0.567926 + 0.567926i
974974 −21.3926 7.28755i −0.685462 0.233508i
975975 11.3799i 0.364448i
976976 26.1708 44.8808i 0.837708 1.43660i
977977 15.3837i 0.492169i 0.969248 + 0.246085i 0.0791441π0.0791441\pi
−0.969248 + 0.246085i 0.920856π0.920856\pi
978978 −8.46334 + 24.8441i −0.270628 + 0.794427i
979979 −46.0796 46.0796i −1.47271 1.47271i
980980 −0.0118326 + 0.00153183i −0.000377979 + 4.89325e-5i
981981 −4.75382 + 4.75382i −0.151778 + 0.151778i
982982 −42.1543 + 20.7317i −1.34520 + 0.661576i
983983 31.2924i 0.998073i −0.866581 0.499037i 0.833687π-0.833687\pi
0.866581 0.499037i 0.166313π-0.166313\pi
984984 8.29581 + 1.67807i 0.264461 + 0.0534948i
985985 1.42513 0.0454084
986986 1.36560 + 2.77671i 0.0434895 + 0.0884283i
987987 3.95631 + 3.95631i 0.125931 + 0.125931i
988988 −15.1954 + 19.7148i −0.483430 + 0.627211i
989989 54.1856 13.0658i 1.72300 0.415468i
990990 −0.265545 + 0.779508i −0.00843959 + 0.0247744i
991991 27.6157i 0.877241i −0.898672 0.438620i 0.855467π-0.855467\pi
0.898672 0.438620i 0.144533π-0.144533\pi
992992 13.0660 + 0.927191i 0.414844 + 0.0294384i
993993 −15.1991 −0.482329
994994 −18.2061 + 53.4438i −0.577461 + 1.69514i
995995 0.718583 + 0.718583i 0.0227806 + 0.0227806i
996996 18.9726 + 14.6233i 0.601170 + 0.463358i
997997 26.4275 + 26.4275i 0.836969 + 0.836969i 0.988459 0.151490i 0.0484072π-0.0484072\pi
−0.151490 + 0.988459i 0.548407π0.548407\pi
998998 −22.5070 45.7640i −0.712445 1.44863i
999999 12.0357i 0.380793i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 368.2.i.b.91.6 yes 80
4.3 odd 2 1472.2.i.b.1103.11 80
16.3 odd 4 inner 368.2.i.b.275.5 yes 80
16.13 even 4 1472.2.i.b.367.12 80
23.22 odd 2 inner 368.2.i.b.91.5 80
92.91 even 2 1472.2.i.b.1103.12 80
368.45 odd 4 1472.2.i.b.367.11 80
368.275 even 4 inner 368.2.i.b.275.6 yes 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
368.2.i.b.91.5 80 23.22 odd 2 inner
368.2.i.b.91.6 yes 80 1.1 even 1 trivial
368.2.i.b.275.5 yes 80 16.3 odd 4 inner
368.2.i.b.275.6 yes 80 368.275 even 4 inner
1472.2.i.b.367.11 80 368.45 odd 4
1472.2.i.b.367.12 80 16.13 even 4
1472.2.i.b.1103.11 80 4.3 odd 2
1472.2.i.b.1103.12 80 92.91 even 2